An error diffusion process is widely used in image display apparatuses and printing apparatuses. This error diffusion process is particularly an important factor for the image quality of inkjet printing apparatuses. Present inkjet printing apparatuses are provided with techniques which express a plurality of gray levels for one pixel by discharging droplets having different sizes onto a sheet. Such techniques typically express three values or four values for a pixel. Three values are expressed by using two sizes of ink droplet, i.e., small and large droplets. Four values are expressed by using three sizes of ink droplet, i.e., small, medium and large droplets. To print images by using such inkjet printing apparatuses, error diffusion is used in converting a multilevel image into a ternary or quaternary image.
Ternarization in the conventional error diffusion is as follows. Two, first and second threshold values are prepared. Assuming that ternary outputs are 0, 1, and 2, if an input is smaller than the first threshold value, the output is 0 (a 0th output value); if an input is equal to or larger than the first threshold value and smaller than the second threshold value, the output is 1 (a first output value); and if an input is equal to or larger than the second threshold value, the output is 2 (a second output value).
To convert the output values of 0, 1, and 2 into pixel values of the input multilevel image data, the general approach is to convert the first output value whose output is 1 into ½ of a maximum value Lmax of the input, and convert the second output value whose output is 2 into the maximum value of the input. That is, output converted values obtained by converting output values into multilevels which input values can take are 0, (Lmax)/2, and Lmax with respect to 0, 1, and 2, respectively. This output converted value is also simply called an output value in some cases. Also, the general method is to set the first threshold value to ¼ the maximum value Lmax of the input and the second threshold value to ¾ the maximum value Lmax of the input, or to set the first threshold value to ⅓ the maximum value Lmax of the input and the second threshold value to ⅔ the maximum value Lmax of the input. The output converted values of the ternary outputs are called a 0th output converted value, first output converted value, and second output converted value.
That is, in conventional ternarization using error diffusion, the relationship between the threshold values and output converted values is(0th output converted value(=blank))<(first threshold value)<(first output converted value)<(second threshold value)<(second output converted value).
Likewise, in conventional quaternarization using error diffusion, the relationship between the output converted values and threshold values is(0th output converted value)<(first threshold value)<(first output converted value)<(second threshold value)<(second output converted value)<(third threshold value)<(third output converted value).
When an error diffusion process is performed by using the threshold values having the above relationship with the output values, no quantization error occurs for a uniform image for which an input value is equal to the first output converted value, so the output image is a uniform image having the first output value. That is, in the conventional relationship between the threshold values and output values, if an input value is equal to or smaller than the first threshold value, an image is formed by pixels having the first output value and blank pixels (the 0th output value), and, if an input value is larger than the first threshold value, an image is formed by pixels having the first output value and pixels having the second output value.
The purpose of this relationship between the threshold values and output values converted into multilevels is to minimize an error between the input level and output level of each pixel.
Unfortunately, when small droplets are used to print pixels having the first output value described above in an inkjet printing apparatus, the printing position accuracy (landing accuracy) of these small droplets becomes lower than that of large droplets. Therefore, unevenness readily occurs if an image is formed by densely gathering small droplets. Also, an error diffusion method forms a pseudo contour on an output image if the value of input data is slightly larger than the output converted value. That is, multilevel inkjet printing apparatuses sometimes deteriorate the image quality.